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Yield Surface (yield + surface)

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Engineering100%

Selected Abstracts

Plasticity-fibre model for steel triangular plate energy dissipating devices

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2002
Chung-Che Chou
Abstract Properly fabricated triangular-plate added damping and stiffness (TADAS) devices can sustain a large number of yield reversals without strength degradation, thereby dissipating a significant amount of earthquake-induced energy. A pronounced isotropic-hardening effect is recognized in the force-deformation relationships of the TADAS devices made from two grades of low yield strength steel. The proposed plasticity-fibre model employing two surfaces (a yield surface and a bounding surface) in plasticity theory accurately predicts the experimental responses of the TADAS devices. This model is also implemented into a computer program DRAIN2D+ to investigate a frame response with the TADAS devices. Substructure pseudo-dynamic tests and analytical studies of a two-storey steel frame constructed with the low yield strength steel, LYP-100 or LYP-235 grade, TADAS devices confirm that the dynamic structural response can only be predicted if the proposed plasticity-fibre model is used for LYP-100 steel TADAS device. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A destructuration theory and its application to SANICLAY model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2010
Mahdi Taiebat
Abstract Many natural clays have an undisturbed shear strength in excess of the remoulded strength. Destructuration modeling provides a means to account for such sensitivity in a constitutive model. This paper extends the SANICLAY model to include destructuration. Two distinct types of destructuration are considered: isotropic and frictional. The former is a concept already presented in relation to other models and in essence constitutes a mechanism of isotropic softening of the yield surface with destructuration. The latter refers to the reduction of the critical stress ratio reflecting the effect of destructuration on the friction angle, and is believed to be a novel proposition. Both the types depend on a measure of destructuration rate expressed in terms of combined plastic volumetric and deviatoric strain rates. The SANICLAY model itself is generalized from its previous form by additional dependence of the yield surface on the third isotropic stress invariant. Such a generalization allows to obtain as particular cases simplified model versions of lower complexity including one with a single surface and associative flow rule, by simply setting accordingly parameters of the generalized version. A detailed calibration procedure of the relatively few model constants is presented, and the performance of three versions of the model, in descending order of complexity, is validated by comparison of simulations to various data for oedometric consolidation followed by triaxial undrained compression and extension tests on two structured clays. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Elasto-plastic analysis of block structures through a homogenization method

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2010
G. de Felice
Abstract The paper describes the development and numerical implementation of a constitutive relationship for modeling the elasto-plastic behavior of block structures with periodic texture, regarded at a macroscopic scale as homogenized anisotropic media. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in an finite element (FE) code by means of two different algorithms: an implicit return mapping scheme and a minimization algorithm directly derived from the Haar,Karman principle. The model is validated against analytical and experimental results: the comparison between the homogenized continuum and the original block assembly shows a good agreement in terms of ultimate inelastic behavior, when the size of the block is small as compared with that of the whole assembly. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Development in modeling cyclic loading of sands based on kinematic hardening

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2009
Mohammad Maleki
Abstract In this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou-Jafari-Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non-associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress,dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Non-uniqueness of critical state line in compression and extension conditions

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2009
Zhen-Yu Yin
Abstract Experimental evidence has indicated that the critical state line determined from undrained compression tests is not identical to that determined from undrained extension tests. The purpose of this paper is to investigate a modelling method that accounts for the non-uniqueness of critical state lines in the compression and the extension testing conditions. Conventional elastic,plastic cap models can predict only a unique critical state line for the compression and the extension tests. A new micromechanical stress,strain model is developed considering explicitly the location of critical state line. The model is then used to simulate undrained triaxial compression and extension tests performed on isotropically consolidated samples with different over-consolidated ratios. The predictions are compared with experimental results as well as that predicted by models with kinematic hardening of yield surface. All simulations demonstrate that the proposed micromechanical approach is capable of modelling the undrained compression and the undrained extension tests. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured clays

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008
Angelo Amorosi
Abstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source]

SANISAND: Simple anisotropic sand plasticity model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2008
Mahdi Taiebat
Abstract SANISAND is the name used for a family of simple anisotropic sand constitutive models developed over the past few years within the framework of critical state soil mechanics and bounding surface plasticity. The existing SANISAND models use a narrow open cone-type yield surface with apex at the origin obeying rotational hardening, which implies that only changes of the stress ratio can cause plastic deformations, while constant stress-ratio loading induces only elastic response. In order to circumvent this limitation, the present member of the SANISAND family introduces a modified eight-curve equation as the analytical description of a narrow but closed cone-type yield surface that obeys rotational and isotropic hardening. This modification enables the prediction of plastic strains during any type of constant stress-ratio loading, a feature lacking from the previous SANISAND models, without losing their well-established predictive capability for all other loading conditions including the cyclic. In the process the plausible assumption is made that the plastic strain rate decomposes in two parts, one due to the change of stress ratio and a second due to loading under constant stress ratio, with isotropic hardening depending on the volumetric component of the latter part only. The model formulation is presented firstly in the triaxial stress space and subsequently its multiaxial generalization is developed following systematically the steps of the triaxial one. A detailed calibration procedure for the model constants is presented, while successful simulation of both drained and undrained behavior of sands under constant and variable stress-ratio loadings at various densities and confining pressures is obtained by the model. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Effective stress concept in unsaturated soils: Clarification and validation of a unified framework

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2008
Mathieu Nuth
Abstract The effective stress principle, conventionally applied in saturated soils, is reviewed for constitutive modelling purposes. The assumptions for the applicability of Terzaghi's single effective stress are recalled and its advantages are inventoried. The possible stress frameworks applicable to unsaturated soil modelling are reassessed in a comparative manner, specifically the Bishop's single effective stress, the independent stress variables approach and the generalized stress framework. The latter considerations lead to the definition of a unified stress context, suitable for modelling soils under different saturation states. In order to qualify the implications brought by the proposed stress framework, several experimental data sets are re-examined in the light of the generalized effective stress. The critical state lines (CSLs) at different saturation states tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress plane. The effective stress interpretation is also applied to isotropic paths and compared with conventional net stress conception. The accent is finally laid on a second key feature for constitutive frameworks based on a unified stress, namely the sufficiency of a unique mechanical yield surface besides the unique CSL. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Thermal effects in partially saturated soils: a constitutive model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2005
Gabriella Bolzon
Abstract The present paper is centred on the assessment of an elastic,plastic model for partially saturated soils, earlier proposed by the authors, for its predictive capability with respect to temperature changes, on the light of available experimental results. The model is cast within a constitutive framework that uses Bishop's stress and suction as main variables governing the volumetric response of the material. Some enhancement to the original temperature-independent formulation is proposed. In particular, functions describing the yield surface and the compressibility modulus are modified to account for the shrinking of the elastic domain and for the increase of irreversible volumetric strain with heating. Some examples illustrate the main features of the present proposal. Comparison with some experimental results is also included. Copyright © 2005 John Wiley & Sons, Ltd. [source]

An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2005
Taha Habiballah
Abstract Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker,Prager yield surface has been used with a non-associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full-scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Generalized strain probing of constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2004
Youssef M. A. Hashash
Abstract Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate-independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane-strain strain probe (PSSP), are used to generate 3-D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto-plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A micromechanical approach to the strength criterion of Drucker-Prager materials reinforced by rigid inclusions

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7-8 2004
Jean-François Barthélémy
Abstract At the microscopic scale, concrete can be considered as a frictional matrix (cement paste) surrounding rigid inclusions (aggregate or sand inclusions). The present paper proposes a theoretical approach to the strength criterion of such a composite material. It is shown that the macroscopic stress states on the yield surface can be obtained from the solution to non-linear viscous problems defined on a representative volume element. The practical determination of the yield surface implements a non-linear homogenization scheme based on the modified secant method. The role of the interface between the matrix and the inclusions is also investigated. Two extreme modellings are considered: perfect bonding and non-frictional interfaces. In both cases, the method yields a macroscopic strength criterion of the Drucker,Prager type. The macroscopic friction angle is a function of that of the matrix and of the volume fraction of the inclusions. In the case of perfect bonding, the inclusions have a reinforcing effect. In contrast, this may not be true for a non-frictional interface. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Gradient plasticity modelling of strain localization in granular materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2004
O. Al Hattamleh
Abstract The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A unified approach to the implicit integration of standard, non-standard and viscous plasticity models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2002
René de Borst
Abstract It is shown how modern concepts to integrate the elasto-plastic rate equations of standard plasticity via an implicit algorithm can be generalized to plasticity without an explicitly defined yield surface and to overstress-type models of viscoplasticity, where the stress point can be located outside the loading surface. For completeness, a tangent operator is derived that is consistent with the update algorithm. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Incrementalization of a single hardening constitutive model for frictional materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2002
P. V. Lade
Abstract The governing equations for an elasto-plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user-defined module for finite element calculations. This isotropic, work-hardening and -softening model employs a single yield surface, it incorporates non-associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three-dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26:661). Copyright © 2002 John Wiley & Sons, Ltd. [source]

Implementation algorithm for a single hardening constitutive model for frictional materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2002
K. P. Jakobsen
Abstract An advanced elasto-plastic constitutive model for frictional materials, whose incremental version is presented in a companion paper (Int. J. Numer. Anal. Meth. Geomech., 2002; 26:647), is implemented in a user-defined material module. The general calculation strategy inside this module is presented and discussed, including the initial intersection of the yield surface and the techniques for updating of stresses and hardening modulus. Several integration schemes are implemented in the module and their capabilities in relation to the advanced, three-dimensional constitutive model are evaluated. The forward Euler, modified Euler, and Runge,Kutta,Dormand,Prince integration schemes are explained in detail, compared, and evaluated in view of error tolerances and computational efficiency. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Inelastic constitutive properties and shear localization in Tennessee marble

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2001
D. J. Holcomb
Abstract The inelastic response of Tennessee marble is modelled by an elastic plastic constitutive relation that includes pressure dependence of yield, strain-softening and inelastic volume strain (dilatancy). Data from 12 axisymmetric compression tests at confining pressures from 0 to 100 MPa are used to determine the dependence of the yield function and plastic potential, which are different, on the first and second stress invariants and the accumulated inelastic shear strain. Because the data requires that the strain at peak stress depends on the mean stress, the locus of peak stresses is neither a yield surface nor a failure envelope, as is often assumed. Based on the constitutive model and Rudnicki and Rice criterion, localization is not predicted to occur in axisymmetric compression although faulting is observed in the tests. The discrepancy is likely due to the overly stiff response of a smooth yield surface model to abrupt changes in the pattern of straining. The constitutive model determined from the axisymmetric compression data describes well the variation of the in-plane stress observed in a plane strain experiment. The out-of-plane stress is not modelled well, apparently because the inelastic normal strain in this direction is overpredicted. In plane strain, localization is predicted to occur close to peak stress, in good agreement with the experiment. Observation of localization on the rising portion of the stress,strain curve in plane strain does not, however, indicate prepeak localization. Because of the rapid increase of mean stress in plane strain, the stress,strain curve can be rising while the shear stress versus shear strain curve at constant mean stress is falling (negative hardening modulus). Copyright © 2001 John Wiley & Sons, Ltd. [source]

Comparison of two different models to account for induced flow anisotropy during complex loading processes

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
Clemens Barthel
Some metals exhibit an increase of the yield stress after orthogonal strain path changes, i.e. so,called cross hardening. Two approaches are discussed in this work which are capable of taking that effect into account in an appropriate manner. The first approach is closely related to that of Teodosiu and Hu. The second model considers besides the movement of the center of the yield surface and its proportional expansion also the change of its shape and is able to describe the induced anisotropic behavior with regard to complicated loading histories. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2007
D. A. Sun
Abstract This paper presents a three-dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled-suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water-retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water-retention behaviour is studied using data obtained from controlled-suction wetting,drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress,strain-strength behaviour and the effect of void ratio on the water-retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three-dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka,Nakai criterion. Model predictions of the stress,strain and water-retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A middle surface concept (MSC) model for saturated sands in general stress space

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2006
Y. Yang
Abstract An elastoplastic constitutive model is proposed for saturated sands in general stress space using the middle surface concept (MSC). In MSC, different features of stress,strain response of a material are divided into different pseudo-yield surfaces. The true-yield surface representing the true response is established by using various links between the yield surfaces. In this MSC sand model, several well-known features of sand response are represented by three different pseudo-yield surfaces, which are developed in a simple and straightforward way. These features include the critical state behaviour, the effects of state parameter, unloading and reloading plastic deformation, the influence of fabric anisotropy, and phase transformation line related behaviour. Finally, the model predictions and test results are compared for two different types of sands under a variety of loading conditions and good comparisons are obtained. The application of MSC to saturated sand modelling shows the versatility of MSC as a general concept for modelling stress,strain response of materials. Copyright © 2006 John Wiley & Sons, Ltd. [source]